FIGS. 1 and 2 show a chainless transmission mechanism for bicycles according to the prior art. This structure of chainless transmission mechanism comprises bottom bracket shell 3A' having a top mounting to BB cap 2A which is welded to the bicycle frame 1A', a axle 4A' fastened to the bottom bracket shell 3A' by bearings 3C' and fastening elements 4B' and 4C', a gear box 6A having a horizontal mounting slot 6C' coupled to the freewheel hub 7A' and covered by a rear cover 6B', a sleeve 5D' connected between the bottom bracket shell 3A' and the gear box 6A' by connectors 3D' and 3E', a transmission shaft 5C' received in the sleeve 5D', a first pair of bevel gears 5A' and 5B' coupled between the axle 4A' and the transmission shaft 5C', and a second pair of bevel gears 5E' and 5F'. When the axle 4A' is rotated, the transmission shaft 5C' is turned by the first pair of bevel gears 5A' and 5B' to rotate the freewheel hub 7A' through the second pair of bevel gears 5E' and 5F'. However, this structure of chainless transmission mechanism is still not satisfactory in function. The drawbacks of this structure of chainless transmission mechanism is outlined hereinafter.
1. The bottom bracket 1B' of the bicycle frame 1A' must be cut away, and then a frame 2A' which fits over the top mounting frame 3B' of the bottom bracket bearing axle holder 3A' must be welded to the bicycle frame 1A' to replace the bottom bracket 1B' for mounting the bottom bracket bearing axle holder 3A'. The bottom bracket shell 3A is fastened to the frame 2A by screw bolts 2B. This arrangement complicates the installation procedure of the chainless transmission mechanism. PA1 2. Because the horizontal mounting slot 6C' of the gear box 6A' is a backward opening, the wheel hub 7A may disconnect from gear box 6A easily when the bicycle runs over a rough road. Furthermore, the rear fender and adjacent parts of the bicycle must be dismounted from the bicycle frame if the wheel hub 7A has to be dismounted from the gear box 6A for a repair work. PA1 3. The bevel gear 5F' which is to be coupled to the freewheel hub 7A' has a coupling portion 7B' in shape and function similar to that of the chain seat for the freewheel gear cluster, and the chain seat of the freewheel hub 7A' must be removed before the installation of the bevel gear 5F'. This arrangement also complicates the installation procedure of the chainless transmission mechanism. When the chain seat of the freewheel hub is removed, it can no longer be used. Furthermore, removing the original chain seat from the freewheel hub will relatively affect the structural strength of the freewheel hub.